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# algebra word problem

During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 7:00am there were 6,000 bacteria present in the culture. At noon, the number of bacteria grew to 6,700. How many bacteria will there be at midnight?

### 2 Answers by Expert Tutors

Michael F. | Mathematics TutorMathematics Tutor
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If the growth rate is proportional to the population, then it is exponential.  That is the number of bacteria at time t, call it B(t)=B(0)ekt.  In our case we have B(t)=6000ekt.  The k is determined by noting that 12 noon, t=5 we have 6700=6000e5k, and so 5k=ln(6700/6000), or k=.022069611433773. At midnight, t=17 hours we have that
B(17)=6000e.37518339...=6000×1.45525827...=8731.549... or about 8732

In no way does this qualify as an algebra word problem, unless you are simply told about the growth and not asked to show it.
SURENDRA K. | An experienced,patient & hardworking tutorAn experienced,patient & hardworking tut...
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At 7am no of bacteria present.       = 6000

At 12 noon no of bacteria present   = 6700

In 5 hours increase in bacteria.       = 6700-6000=700

In one hour increase in bacteria       = 700/5=140

In 12 hours(at mid night) increase in bacteria.      = 140*12=      1680

So, no of bacteria present at midnight. = 6700+1680=8380